Multi-Hypothesis Topological Isomorphism Matching Method for Synthetic Aperture Radar Images with Large Geometric Distortion

The dramatic undulations of a mountainous terrain will introduce large geometric distortions in each Synthetic Aperture Radar (SAR) image with different look angles, resulting in a poor registration performance. To this end, this paper proposes a multi-hypothesis topological isomorphism matching method for SAR images with large geometric distortions. The method includes the Ridge-Line Keypoint Detection (RLKD) and Multi-Hypothesis Topological Isomorphism Matching (MHTIM). Firstly, based on the analysis of the ridge structure, a ridge keypoint detection module and a keypoint similarity description method are designed, which aim to quickly produce a small number of stable matching keypoint pairs under large look angle differences and large terrain undulations. The keypoint pairs are further fed into the MHTIM module. Subsequently, the MHTIM method is proposed, which uses the stability and isomorphism of the topological structure of the keypoint set under different perspectives to generate a variety of matching hypotheses, and iteratively achieves the keypoint matching. This method uses both local and global geometric relationships between two keypoints, hence it achieving better performance compared with traditional methods. We tested our approach on both simulated and real mountain SAR images with different look angles and different elevation ranges. The experimental results demonstrate the effectiveness and stable matching performance of our approach.

Relations on topologized groups

: In our present paper, topological groups are being discussed, where the relations with counter examples built the interest in the generalized structure. Some of these structures have also been converted into the other structures using topological isomorphism. In our work, the identity element plays the important role in lieu of arbitrary element. The role of topology has the more interest in our discipline.

Groupoids associated to inverse semigroups

<p>Starting with an arbitrary inverse semigroup with zero, we study two well-known groupoid constructions, yielding groupoids of filters and groupoids of germs. The groupoids are endowed with topologies making them étale. We use the bisections of the étale groupoids to show there is a topological isomorphism between the groupoids. This demonstrates a widely useful equivalence between filters and germs. We use the isomorphism to characterise Exel’s tight groupoid of germs as a groupoid of filters, to find a nice basis for the topology on the groupoid of ultrafilters and to describe the ultrafilters in the inverse semigroup of an arbitrary self-similar group.</p>

Groupoids associated to inverse semigroups

<p>Starting with an arbitrary inverse semigroup with zero, we study two well-known groupoid constructions, yielding groupoids of filters and groupoids of germs. The groupoids are endowed with topologies making them étale. We use the bisections of the étale groupoids to show there is a topological isomorphism between the groupoids. This demonstrates a widely useful equivalence between filters and germs. We use the isomorphism to characterise Exel’s tight groupoid of germs as a groupoid of filters, to find a nice basis for the topology on the groupoid of ultrafilters and to describe the ultrafilters in the inverse semigroup of an arbitrary self-similar group.</p>

Multiphase Open Phase Processes Differential Equations

The thermodynamic approach for the description of multiphase open phase processes is developed based on van der Waals equation in the metrics of Gibbs and incomplete Gibbs potentials. Examples of thermodynamic modeling of the multiphase and multicomponent A3B5 systems (In-Ga-As-Sb and In-P-As-Sb) and Na+, K+, Mg2+, Ca2+//Cl−, SO42−-H2O water–salt system are presented. Topological isomorphism of different type phase diagrams is demonstrated.

THE COMPLEXITY OF TOPOLOGICAL GROUP ISOMORPHISM

We study the complexity of the topological isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Borel spaces. For profinite, locally compact, and Roelcke precompact groups, we show that the complexity is the same as the one of countable graph isomorphism. For oligomorphic groups, we merely establish this as an upper bound.

Unitary completions of locally algebraic and locally analytic principal series of p-adic GL2

We generalize a result of Emerton on the relationship between unitary completions of locally [Formula: see text]-analytic and locally [Formula: see text]-algebraic principal series representations induced from certain locally [Formula: see text]-algebraic characters of the diagonal torus of [Formula: see text], where [Formula: see text] is a finite extension of [Formula: see text]. Namely, under a non-critical slope hypothesis on the character being induced, the map on universal unitary completions arising from the inclusion of the locally algebraic induction into the locally analytic induction is a topological isomorphism. (Emerton proved this result for [Formula: see text].) The main ingredients in carrying out a “several-variable” version of Emerton’s argument are the description of the local convex space of locally [Formula: see text]-analytic functions on the group [Formula: see text] in terms of the embeddings of [Formula: see text] into our [Formula: see text]-adic coefficient field, and a generalization by Breuil of the classical result of Amice-Vélu and Vishik on “tempered distributions” on [Formula: see text].